A novel immune genetic algorithm with the elitist selection and elitist crossover was proposed,which is called the immune genetic algorithm with the elitism (IGAE).In IGAE,the new methods for computing antibody similarity,expected reproduction probability,and clonal selection probability were given.IGAE has three features.The first is that the similarities of two antibodies in structure and quality are all defined in the form of percentage,which helps to describe the similarity of two antibodies more accurately and to reduce the computational burden effectively.The second is that with the elitist selection and elitist crossover strategy IGAE is able to find the globally optimal solution of a given problem.The third is that the formula of expected reproduction probability of antibody can be adjusted through a parameter β,which helps to balance the population diversity and the convergence speed of IGAE so that IGAE can find the globally optimal solution of a given problem more rapidly.Two different complex multi-modal functions were selected to test the validity of IGAE.The experimental results show that IGAE can find the globally maximum/minimum values of the two functions rapidly.The experimental results also confirm that IGAE is of better performance in convergence speed,solution variation behavior,and computational efficiency compared with the canonical genetic algorithm with the elitism and the immune genetic algorithm with the information entropy and elitism.